Identifying networks with common organizational principles

Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to sophisticated but computationally costly alignment-based approaches. Yet it remains challenging to accurately cluster networks that are of a different size and density, but hypothesized to be structurally similar. In this paper, we address this problem by introducing a new network comparison methodology that is aimed at identifying common organizational principles in networks. The methodology is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.Comment: 26 pages, 7 figure

Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Probabilistic methods in the analysis of protein interaction networks

Imperial Users onl

Dynamic-Based Structure Measures of Complex Networks

Ph.DDOCTOR OF PHILOSOPH

An analysis of age-related alterations in functional memory networks

The human brain is the most complex organ of the human body and many aspects of its functioning have not yet been understood. One of the most fascinating abilities of the human brain is the skill to store and retrieve information, which is what we refer to as memory. One attempt to get a deeper insight into the functioning of memory is to analyze the complex activity pattern of the human brain that emerges while a memory task is being processed. The understanding of memory is epistemologically very intriguing since it is this ability that enables us to collect, to store and to recall ideas, emotions and thoughts - hence, it builds our own identity. This thesis analyses age-related changes in functional connectivity networks related to episodic and working memory processing. The data for this study were measured using fMRI technique and the sample set consisted of healthy individuals aging from 20 up to over 80 years. Based on the fMRI data we construct correlation networks by correlating pairwisely the measured voxel activity, the nodes of the network being brain voxels, the edges being correlations. These networks are thresholded, anatomically clustered and analyzed by computing statistical network measures, using spectral methods, computing network entropy and calculating persistent homology. The main findings are: elderly individuals exhibit expanded neural networks with less differentiation between episodic and working memory tasks. However, we observe compensatory mechanisms that accompany this dedifferentiation process. Network synchronizability is higher for elderly individuals. Network entropy increases as well with age, yielding a lower network vulnerability for elderly individuals. Aging processes leave traces in the homology pattern of the networks, whereas all brain networks exhibit different persistent homology features

Topological evolution of networks : case studies in the US airlines and language Wikipedias

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 195-198).This thesis examines the topology of engineering systems and how that topology changes over time. Topology refers to the relative arrangement and connectivity of the elements of a system. We review network theory relevant to topological evolution and use graph-theoretical methods to analyze real systems, represented as networks. Using existing graph generative models, we develop a profile of canonical graphs and tools to compare a real network to that profile. The developed metrics are used to track topology changes over the history of real networks. This theoretical work is applied to two case studies. The first discusses the US airline industry in terms of routes. We study various airlines and segments of the industry statistically and find commonly occurring patterns. We show that there are topology transitions in the history of airlines in the period 1990-2007. Most airline networks have similar topology and historical patterns, with the exception of Southwest Airlines. We show mathematically that Southwest's topology is different. We propose two heuristic growth models, one featuring hub-seeding derived from the underlying patterns of evolution of JetBlue Airways and one featuring local interconnectedness, derived from the patterns of growth of Southwest. The two models match the topologies of these airlines better than canonical models over time. Results suggest that Southwest is becoming more centralized, closer to the hub-spoke topologies of other airlines. Our second case study discusses the growth of language Wikipedia networks, where nodes are articles and hyperlinks are the connections between them. These knowledge networks are subject to different constraints than air transportation systems. The topology of these networks and their growth principles are completely different. Most Wikipedias studied grow by coalescence, with multiple disconnected thematic clusters of pages growing separately and over time, converging to a giant connected component via weak links. These topologies start out as simple trees, and coalesce into sparse hierarchical structures with random interlinking. One striking exception is the history of the Chinese Wikipedia, which grows fully connected from its inception. We discuss these patterns of growth comparatively across Wikipedias, and in general, compared to airline networks. Our work suggests that complex engineering systems are hybrids of pure canonical forms and that they undergo distinct phase transitions during their evolution. We find commonality among systems and uncover important differences by learning from the exceptions.by Gergana Assenova Bounova.Ph.D